## 1xN plasmonic power splitters based on metal-insulator-metal waveguides |

Optics Express, Vol. 21, Issue 4, pp. 4036-4043 (2013)

http://dx.doi.org/10.1364/OE.21.004036

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### Abstract

Novel plasmonic power splitters constructed from a rectangular ring resonator with direct-connected input and output waveguides are presented and numerically investigated. An analytical model and systematic approach for obtaining the appropriate design parameters are developed by designing an equivalent lumped circuit model for the transmission lines and applying it to plasmonic waveguides. This approach can dramatically reduce simulation times required for determining the desired locations of the output waveguides. Three examples are shown, the 1 × 3, 1 × 4, and 1 × 5 equal-power splitters, with the design method being easily extended to any number of output ports.

© 2013 OSA

## 1. Introduction

1. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science **311**(5758), 189–193 (2006). [CrossRef] [PubMed]

2. R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today **9**(7–8), 20–27 (2006). [CrossRef]

3. T. W. Lee and S. Gray, “Subwavelength light bending by metal slit structures,” Opt. Express **13**(24), 9652–9659 (2005). [CrossRef] [PubMed]

4. G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. **87**(13), 131102 (2005). [CrossRef]

5. R. J. Walters, R. V. A. van Loon, I. Brunets, J. Schmitz, and A. Polman, “A silicon-based electrical source of surface plasmon polaritons,” Nat. Mater. **9**(1), 21–25 (2010). [CrossRef] [PubMed]

6. P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, “Electrical detection of confined gap plasmons in metal-insulator-metal waveguides,” Nat. Photonics **3**(5), 283–286 (2009). [CrossRef]

7. X. S. Lin and X. G. Huang, “Tooth-shaped plasmonic waveguide filters with nanometeric sizes,” Opt. Lett. **33**(23), 2874–2876 (2008). [CrossRef] [PubMed]

8. J. Tao, X. G. Huang, X. S. Lin, Q. Zhang, and X. Jin, “A narrow-band subwavelength plasmonic waveguide filter with asymmetrical multiple-teeth-shaped structure,” Opt. Express **17**(16), 13989–13994 (2009). [CrossRef] [PubMed]

9. J. Q. Liu, L. L. Wang, M. D. He, W. Q. Huang, D. Wang, B. S. Zou, and S. Wen, “A wide bandgap plasmonic Bragg reflector,” Opt. Express **16**(7), 4888–4894 (2008). [CrossRef] [PubMed]

10. A. Hosseini and Y. Massoud, “A low-loss metal-insulator-metal plasmonic Bragg reflector,” Opt. Express **14**(23), 11318–11323 (2006). [CrossRef] [PubMed]

4. G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. **87**(13), 131102 (2005). [CrossRef]

11. S. Passinger, A. Seidel, C. Ohrt, C. Reinhardt, A. Stepanov, R. Kiyan, and B. Chichkov, “Novel efficient design of Y-splitter for surface plasmon polariton applications,” Opt. Express **16**(19), 14369–14379 (2008). [CrossRef] [PubMed]

14. Y. Guo, L. Yan, W. Pan, B. Luo, K. Wen, Z. Guo, H. Li, and X. Luo, “A plasmonic splitter based on slot cavity,” Opt. Express **19**(15), 13831–13838 (2011). [CrossRef] [PubMed]

4. G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. **87**(13), 131102 (2005). [CrossRef]

11. S. Passinger, A. Seidel, C. Ohrt, C. Reinhardt, A. Stepanov, R. Kiyan, and B. Chichkov, “Novel efficient design of Y-splitter for surface plasmon polariton applications,” Opt. Express **16**(19), 14369–14379 (2008). [CrossRef] [PubMed]

12. N. Nozhat and N. Granpayeh, “Analysis of the plasmonic power splitter and MUX/DEMUX suitable for photonic integrated circuits,” Opt. Commun. **284**(13), 3449–3455 (2011). [CrossRef]

13. Z. Han and S. He, “Multimode interference effect in plasmonic subwavelength waveguides and an ultra-compact power splitter,” Opt. Commun. **278**(1), 199–203 (2007). [CrossRef]

14. Y. Guo, L. Yan, W. Pan, B. Luo, K. Wen, Z. Guo, H. Li, and X. Luo, “A plasmonic splitter based on slot cavity,” Opt. Express **19**(15), 13831–13838 (2011). [CrossRef] [PubMed]

12. N. Nozhat and N. Granpayeh, “Analysis of the plasmonic power splitter and MUX/DEMUX suitable for photonic integrated circuits,” Opt. Commun. **284**(13), 3449–3455 (2011). [CrossRef]

13. Z. Han and S. He, “Multimode interference effect in plasmonic subwavelength waveguides and an ultra-compact power splitter,” Opt. Commun. **278**(1), 199–203 (2007). [CrossRef]

14. Y. Guo, L. Yan, W. Pan, B. Luo, K. Wen, Z. Guo, H. Li, and X. Luo, “A plasmonic splitter based on slot cavity,” Opt. Express **19**(15), 13831–13838 (2011). [CrossRef] [PubMed]

## 2. Design of plasmonic power splitters

15. J. Liu, H. Zhao, Y. Zhang, and S. Liu, “Resonant cavity based antireflection structures for surface plasmon waveguides,” Appl. Phys. B **98**(4), 797–802 (2010). [CrossRef]

_{r}and w, respectively. The corresponding lengths are L

_{r1}and L

_{r2}, respectively.

16. P. Ginzburg and M. Orenstein, “Plasmonic transmission lines: from micro to nano scale with λ/4 impedance matching,” Opt. Express **15**(11), 6762–6767 (2007). [CrossRef] [PubMed]

17. S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, “Transmission line and equivalent circuit models for plasmonic waveguide components,” IEEE J. Sel. Top. Quantum Electron. **14**(6), 1462–1472 (2008). [CrossRef]

_{m}is represented by an equivalent T-lumped circuit model with lumped parameters of Z

_{a,m}and Z

_{b,m}, for m = 1, 2, …, and N + 1 [18]. These parameters are expressed as follows: where β

_{r}is the propagation constant of the line, and Z

_{o}is the characteristic impedance of the transmission line, calculated by

_{in}and frequency of incidence ω [16

16. P. Ginzburg and M. Orenstein, “Plasmonic transmission lines: from micro to nano scale with λ/4 impedance matching,” Opt. Express **15**(11), 6762–6767 (2007). [CrossRef] [PubMed]

17. S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, “Transmission line and equivalent circuit models for plasmonic waveguide components,” IEEE J. Sel. Top. Quantum Electron. **14**(6), 1462–1472 (2008). [CrossRef]

_{m,1}which is proportional to the propagation voltage V

_{m}on the transmission line of the m-th port as all the output ports are terminated in matched loads Z

_{o}. Thus, to obtain equal power at all the output ports, the amplitude of the voltage ratio at any two output ports should be 1.

_{1}= L

_{N + 1}, L

_{2}= L

_{N}…, V

_{2}= V

_{N + 1}, V

_{3}= V

_{N}…. Then, the analysis of the lumped circuit can be simplified, as shown in Fig. 3(a) and 3(b) which are the simplified circuit models looking from the port 1 with odd N and even N, respectively, without including the AR structure. Let M = N/2 for even N and M = (N + 1)/2 for odd N. We define VR(m) as the ratio of the voltage V

_{m + 1}to V

_{m}which iswhere Z

_{eq,m + 1}is the equivalent impedance as seen from the (m + 1)-th port, calculated by

_{1}, L

_{2}, …, and L

_{m}. Accordingly, step by step, we can achieve all amplitudes of VR equal to 1. First, we start by finding the appropriate line length of L

_{M}to achieve the amplitude of VR(M) equal to 1, which is only a function of L

_{M}. In the case that N is even, we can arbitrarily choose the line length of L

_{M + 1}to decide the value of Z

_{eq,M + 1}. Next, we determine the line length of L

_{M-1}such that the amplitude of VR(M-1) is 1, which becomes a function of the single variable L

_{M-1}as L

_{M}is selected. Successively, we repeat the previous procedure recursively to find the other line lengths except for L

_{1}.

_{11}expressed aswhere Z

_{in}is the equivalent input impedance of this whole structure, which is

_{1}are known, L

_{1}becomes the only variable of S

_{11}. To diminish the reflected power at port 1, we can select the line length of L

_{1}to have the minimal amplitude of S

_{11}. However, sometimes the minimal amplitude of S

_{11}is unacceptable, and then the AR structure is applied to effectively mitigate the reflected power without changing all the values of VRs. In the following section, we numerically explore several designs to illustrate the above-mentioned design concepts.

## 3. Numerical results

19. A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. **37**(22), 5271–5283 (1998). [CrossRef] [PubMed]

_{∞}= 1.0 is the relative permittivity in the infinity frequency, ω

_{p}= 1.258 × 10

^{16}rad/sec is the bulk plasma frequency, and γ = 7.295 × 10

^{13}rad/sec is a damping constant. ω

_{n}, γ

_{n}and Δε

_{n}are the oscillator resonant frequencies,

^{the damping factors}and weighting factors associated with the Lorentzian peaks, respectively. All the parameters of this Drude - Lorentz model can be found in Ref [19

19. A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. **37**(22), 5271–5283 (1998). [CrossRef] [PubMed]

_{0}of 1550 nm. A 50 nm perfectly matched layer (PML) boundary with reflectivity of 10

^{−8}is applied. The grid sizes in the transverse direction, x, and transmission direction, z, are Δx = Δz = 5 nm. As the grid sizes are smaller than 5 nm, the transmission varies within ± 2%.

### 3.1 Odd N

_{2}. Figure 4(a) shows the amplitude of VR(2) for varying line length L

_{2}. As we can see, the amplitude of VR(2) oscillates with a period of 550 nm, corresponding to an optical length of a half λ

_{0}. Furthermore, the amplitude of oscillation gradually decreases because of the complex propagation constant. The amplitude of VR(2) equals 1 when L

_{2}equals 0, 515 nm, 588 nm, etc. Let L

_{2}be 515nm, then the amplitude variation of S

_{11}on L

_{1}is illustrated in Fig. 4(b). A periodic oscillation between 0 and 1 with increasing L

_{1}is observed and the local minima are obtained at L

_{1}= 260 + 550 ×

*l*nm, with

*l*= 0, 1, 2…. As shown in Fig. 4(b), the minimum value is approximately 0.14, which is unsatisfactory for a power splitter. Let L and W be 295 and 1030 nm, respectively, corresponding to L

_{1}of 810 nm and L

_{2}of 515 nm. Then, the reflection at λ

_{0}is mitigated as W

_{r}, L

_{r1}and L

_{r2}are 100, 30 and 155 nm, respectively.

_{0}. The reflected power is effectively reduced to −48.15 dB. The insertion loss of this device is −0.63 dB, mainly resulting from the transmission loss propagating through the ring and AR resonator structures. Figure 4(d) depicts the wavelength dependence of the powers at the ports 1, 2 and 3, calculated both by the TL model and by the FDTD method. As shown, the two simulated results are in close agreement. Moreover, the simulated output powers at the ports 2 and 3 are very close to each other over the broad wavelength range of 1400 to 1700 nm. On the other hand, the reflection is very wavelength selective with a steep V-shaped spectral curve. The bandwidth for reflection less than −20 dB is obtained over a wavelength range of 1460 to 1630 nm.

_{3}to be 515 nm to achieve the amplitude of VR(3) of 1. Then, we search for the line length of L

_{2}to obtain the amplitude of VR(2) equal to 1. Figure 5(a) shows the amplitude variation of VR(2) with L

_{3}of 515 nm on L

_{2}. An oscillation with a period of 550 nm is observed, and the amplitude of VR(2) becomes 1 only as L

_{2}= 0 nm. Let L

_{2}= 0 nm and L

_{3}= 515 nm. The corresponding line lengths of L

_{1}to acquire the minimal amplitude of S

_{11}are 270 + 550 ×

*l*nm, with

*l*= 0, 1, 2…, as illustrated in Fig. 5(b). The reflection can be further minimized as W

_{r}, L

_{r1}and L

_{r2}are 40, 45 and 115 nm, respectively.

_{1}of 820 nm, L

_{2}of 0 nm and L

_{3}of 515 nm. The transmitted powers obtained by the FDTD method are −7.78, −7.62, −7.70, −7.62 and −7.78 dB with respect to output ports 2, 3, 4, 5 and 6. The reflected power is effectively reduced to −69.07 dB. The insertion loss of this device is −0.70 dB. Figure 5(d) depicts the power at the ports 1, 2, 3, and 4 as a function of wavelength. The performance has similar tendencies as those obtained in the aforementioned 1 × 3 power splitter except that the transmission is smaller, roughly less by −2.3 dB. The bandwidth for reflection less than −20 dB is obtained over a wavelength range of 1520 to 1580 nm.

### 4.2 Even N

_{3}to acquire the value of Z

_{eq,3}. Figure 6(a) illustrates the amplitude of VR(2) as the line length L

_{2}is varied at L

_{3}= 250 nm. The amplitude of VR(2) oscillates with period of 550 nm and becomes 1 as L

_{2}is 0, 200 nm, 557 nm, …. Let L

_{2}be 200 nm, and then the amplitude variation of S

_{11}on L

_{1}is displayed in Fig. 6(b). It shows the local minima at L

_{1}= 239 + 550 ×

*l*nm,

*l*= 0, 1, 2…. Let L and W be 464 and 650 nm, respectively, corresponding to L

_{1}of 789 nm, L

_{2}of 200 nm and L

_{3}of 250 nm. The reflection is minimized as W

_{r}, L

_{r1}and L

_{r2}are 185, 0 and 30 nm, respectively. Figure 6(c) shows the layout and the field evolution of this 1 × 4 power splitter. The transmitted powers are −6.76, −6.51, −6.51, and −6.76 dB with respect to the output ports 2, 3, 4, and 5. The reflected power is reduced to −38.89 dB. The insertion loss of this device is −0.61 dB. Figure 6(d) depicts the power at the ports 1, 2, and 3 as a function of wavelength. The calculated transmission spectra obtained by the FDTD method is shifted to shorter wavelengths by roughly 35 nm compared with those obtained by the TL model. The bandwidth for reflection less than −20 dB is obtained over a wavelength range of 1520 to 1580 nm.

## 4. Conclusion

## References and links

1. | E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science |

2. | R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today |

3. | T. W. Lee and S. Gray, “Subwavelength light bending by metal slit structures,” Opt. Express |

4. | G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. |

5. | R. J. Walters, R. V. A. van Loon, I. Brunets, J. Schmitz, and A. Polman, “A silicon-based electrical source of surface plasmon polaritons,” Nat. Mater. |

6. | P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, “Electrical detection of confined gap plasmons in metal-insulator-metal waveguides,” Nat. Photonics |

7. | X. S. Lin and X. G. Huang, “Tooth-shaped plasmonic waveguide filters with nanometeric sizes,” Opt. Lett. |

8. | J. Tao, X. G. Huang, X. S. Lin, Q. Zhang, and X. Jin, “A narrow-band subwavelength plasmonic waveguide filter with asymmetrical multiple-teeth-shaped structure,” Opt. Express |

9. | J. Q. Liu, L. L. Wang, M. D. He, W. Q. Huang, D. Wang, B. S. Zou, and S. Wen, “A wide bandgap plasmonic Bragg reflector,” Opt. Express |

10. | A. Hosseini and Y. Massoud, “A low-loss metal-insulator-metal plasmonic Bragg reflector,” Opt. Express |

11. | S. Passinger, A. Seidel, C. Ohrt, C. Reinhardt, A. Stepanov, R. Kiyan, and B. Chichkov, “Novel efficient design of Y-splitter for surface plasmon polariton applications,” Opt. Express |

12. | N. Nozhat and N. Granpayeh, “Analysis of the plasmonic power splitter and MUX/DEMUX suitable for photonic integrated circuits,” Opt. Commun. |

13. | Z. Han and S. He, “Multimode interference effect in plasmonic subwavelength waveguides and an ultra-compact power splitter,” Opt. Commun. |

14. | Y. Guo, L. Yan, W. Pan, B. Luo, K. Wen, Z. Guo, H. Li, and X. Luo, “A plasmonic splitter based on slot cavity,” Opt. Express |

15. | J. Liu, H. Zhao, Y. Zhang, and S. Liu, “Resonant cavity based antireflection structures for surface plasmon waveguides,” Appl. Phys. B |

16. | P. Ginzburg and M. Orenstein, “Plasmonic transmission lines: from micro to nano scale with λ/4 impedance matching,” Opt. Express |

17. | S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, “Transmission line and equivalent circuit models for plasmonic waveguide components,” IEEE J. Sel. Top. Quantum Electron. |

18. | K. Chang and L. H. Hsieh, |

19. | A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. |

**OCIS Codes**

(130.3120) Integrated optics : Integrated optics devices

(240.6680) Optics at surfaces : Surface plasmons

(310.2790) Thin films : Guided waves

(350.4010) Other areas of optics : Microwaves

**ToC Category:**

Integrated Optics

**History**

Original Manuscript: November 16, 2012

Revised Manuscript: January 31, 2013

Manuscript Accepted: February 4, 2013

Published: February 11, 2013

**Citation**

Chyong-Hua Chen and Kao-Sung Liao, "1xN plasmonic power splitters based on metal-insulator-metal waveguides," Opt. Express **21**, 4036-4043 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-4-4036

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### References

- E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science311(5758), 189–193 (2006). [CrossRef] [PubMed]
- R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today9(7–8), 20–27 (2006). [CrossRef]
- T. W. Lee and S. Gray, “Subwavelength light bending by metal slit structures,” Opt. Express13(24), 9652–9659 (2005). [CrossRef] [PubMed]
- G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett.87(13), 131102 (2005). [CrossRef]
- R. J. Walters, R. V. A. van Loon, I. Brunets, J. Schmitz, and A. Polman, “A silicon-based electrical source of surface plasmon polaritons,” Nat. Mater.9(1), 21–25 (2010). [CrossRef] [PubMed]
- P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, “Electrical detection of confined gap plasmons in metal-insulator-metal waveguides,” Nat. Photonics3(5), 283–286 (2009). [CrossRef]
- X. S. Lin and X. G. Huang, “Tooth-shaped plasmonic waveguide filters with nanometeric sizes,” Opt. Lett.33(23), 2874–2876 (2008). [CrossRef] [PubMed]
- J. Tao, X. G. Huang, X. S. Lin, Q. Zhang, and X. Jin, “A narrow-band subwavelength plasmonic waveguide filter with asymmetrical multiple-teeth-shaped structure,” Opt. Express17(16), 13989–13994 (2009). [CrossRef] [PubMed]
- J. Q. Liu, L. L. Wang, M. D. He, W. Q. Huang, D. Wang, B. S. Zou, and S. Wen, “A wide bandgap plasmonic Bragg reflector,” Opt. Express16(7), 4888–4894 (2008). [CrossRef] [PubMed]
- A. Hosseini and Y. Massoud, “A low-loss metal-insulator-metal plasmonic Bragg reflector,” Opt. Express14(23), 11318–11323 (2006). [CrossRef] [PubMed]
- S. Passinger, A. Seidel, C. Ohrt, C. Reinhardt, A. Stepanov, R. Kiyan, and B. Chichkov, “Novel efficient design of Y-splitter for surface plasmon polariton applications,” Opt. Express16(19), 14369–14379 (2008). [CrossRef] [PubMed]
- N. Nozhat and N. Granpayeh, “Analysis of the plasmonic power splitter and MUX/DEMUX suitable for photonic integrated circuits,” Opt. Commun.284(13), 3449–3455 (2011). [CrossRef]
- Z. Han and S. He, “Multimode interference effect in plasmonic subwavelength waveguides and an ultra-compact power splitter,” Opt. Commun.278(1), 199–203 (2007). [CrossRef]
- Y. Guo, L. Yan, W. Pan, B. Luo, K. Wen, Z. Guo, H. Li, and X. Luo, “A plasmonic splitter based on slot cavity,” Opt. Express19(15), 13831–13838 (2011). [CrossRef] [PubMed]
- J. Liu, H. Zhao, Y. Zhang, and S. Liu, “Resonant cavity based antireflection structures for surface plasmon waveguides,” Appl. Phys. B98(4), 797–802 (2010). [CrossRef]
- P. Ginzburg and M. Orenstein, “Plasmonic transmission lines: from micro to nano scale with λ/4 impedance matching,” Opt. Express15(11), 6762–6767 (2007). [CrossRef] [PubMed]
- S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, “Transmission line and equivalent circuit models for plasmonic waveguide components,” IEEE J. Sel. Top. Quantum Electron.14(6), 1462–1472 (2008). [CrossRef]
- K. Chang and L. H. Hsieh, Microwave Ring Circuits and Related Structures (Wiley, 2004).
- A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt.37(22), 5271–5283 (1998). [CrossRef] [PubMed]

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